From http://cubapolidata.com/tag/venezuelan-coast/ :
“On 22 September Russian Naval cruiser, Peter the Great, set sail with two other ships for Venezuela where they will take part in naval exercises in the Caribbean. Russian bombers recently left Venezuela after a number of training missions off the Venezuelan coast, and a long time Russian spy, now Deputy Prime Minister, Igor Sechin recently made his rounds through Cuba, Venezuela, and Nicaragua at the head of a large delegation of diplomats and business leaders.”
Basically, Russia is courting South America much as it courted Cuba throughout the 1960s, thus attempting to remove U.S. influence in the area. Per the Monroe Doctrine the U.S. vowed to always help out the other countries in the Western Hemisphere but with George Bush busy alienating Latin American countries and with our history of overstepping our permissions, Russia (and China also) see a chance to step in and gain influence and allies.
Venezuela is most receptive right now because Chavez despises the U.S. and has strong Socialist leanings.
If you go to the link there is additional discussion about the reasons and the effects. I only abstracted the actual basic facts about Russian military training events in and near Venezuela.